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Wyszukujesz frazę "Denecke, Klaus" wg kryterium: Autor

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    Wyświetlanie 1-15 z 15
    Tytuł:
    Tree transformations defined by hypersubstitutions
    Autorzy:
    Arworn, Sr.
    Denecke, Klaus
    Powiązania:
    https://bibliotekanauki.pl/articles/728728.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitution
    tree transformation
    tree transducer
    Opis:
    Tree transducers are systems which transform trees into trees just as automata transform strings into strings. They produce transformations, i.e. sets consisting of pairs of trees where the first components are trees belonging to a first language and the second components belong to a second language. In this paper we consider hypersubstitutions, i.e. mappings which map operation symbols of the first language into terms of the second one and tree transformations defined by such hypersubstitutions. We prove that the set of all tree transformations which are defined by hypersubstitutions of a given type forms a monoid with respect to the composition of binary relations which is isomorphic to the monoid of all hypersubstitutions of this type. We characterize transitivity, reflexivity and symmetry of tree transformations by properties of the corresponding hypersubstitutions. The results will be applied to languages built up by individual variables and one operation symbol of arity n ≥ 2.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 219-227
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hyperidentities in many-sorted algebras
    Autorzy:
    Denecke, Klaus
    Lekkoksung, Somsak
    Powiązania:
    https://bibliotekanauki.pl/articles/728740.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitution
    hyperidentity
    heterogeneous algebra
    Opis:
    The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure operators can be applied to characterize solid varieties, i.e., varieties in which every identity is satisfied as a hyperidentity (see [4]). The aim of this paper is to apply the theory of conjugate pairs of additive closure operators to many-sorted algebras.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2009, 29, 1; 47-74
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The order of normalform hypersubstitutions of type (2)
    Autorzy:
    Denecke, Klaus
    Mahdavi, Kazem
    Powiązania:
    https://bibliotekanauki.pl/articles/728816.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitutions
    terms
    idempotent elements
    elements of infinite order
    Opis:
    In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 183-192
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nd-solid varieties
    Autorzy:
    Denecke, Klaus
    Glubudom, Prisana
    Powiązania:
    https://bibliotekanauki.pl/articles/728884.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Non-deterministic hypersubstitution
    conjugate pair of additive closure operators
    M-solid non-deterministic variety
    Opis:
    A non-deterministic hypersubstitution maps any operation symbol of a tree language of type τ to a set of trees of the same type, i.e. to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities. We define the application of a non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras. Non-deterministic hypersubstitutions can also be applied to equations of type τ. Formally, we obtain two closure operators which turn out to form a conjugate pair of completely additive closure operators. This allows us to use the theory of conjugate pairs of additive closure operators for a characterization of M-solid non-deterministic varieties of algebras. As an application we consider M-solid non-deterministic varieties of semigroups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2007, 27, 2; 245-262
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Locally finite M-solid varieties of semigroups
    Autorzy:
    Denecke, Klaus
    Pibaljommee, Bundit
    Powiązania:
    https://bibliotekanauki.pl/articles/728932.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    locally finite variety
    finitely based variety
    M-solidvariety
    Opis:
    An algebra of type τ is said to be locally finite if all its finitely generated subalgebras are finite. A class K of algebras of type τ is called locally finite if all its elements are locally finite. It is well-known (see [2]) that a variety of algebras of the same type τ is locally finite iff all its finitely generated free algebras are finite. A variety V is finitely based if it admits a finite basis of identities, i.e. if there is a finite set σ of identities such that V = ModΣ, the class of all algebras of type τ which satisfy all identities from Σ. Every variety which is generated by a finite algebra is locally finite. But there are finite algebras which are not finitely based. For semigroup varieties, Perkins proved that the variety generated by the five-element Brandt-semigroup
    $B¹₂ = { \begin{pmatrix} 0 & 0 \\ 0 & 0\end{pmatrix}, \begin{pmatrix} 1 & 0 \\ 0 & 0\end{pmatrix}, \begin{pmatrix} 0 & 1 \\ 0 & 0\end{pmatrix}, \begin{pmatrix} 0 & 0 \\ 1 & 0\end{pmatrix}, \begin{pmatrix} 0 & 0 \\ 0 & 1\end{pmatrix}}$
    is not finitely based ([9], [10]). An identity s ≈ t is called a hyperidentity of a variety V if whenever the operation symbols occurring in s and in t, respectively, are replaced by any terms of V of the appropriate arity, the identity which results, holds in V. A variety V is called solid if every identity of V also holds as a hyperidentity in V. If we apply only substitutions from a set M we speak of M-hyperidentities and M-solid varieties. In this paper we use the theory of M-solid varieties to prove that a type (2) M-solid variety of the form $V = H_{M}Mod{F(x₁,F(x₂,x₃)) ≈ F(F(x₁,x₂),x₃)}$, which consists precisely of all algebras which satisfy the associative law as an M -hyperidentity is locally finite iff the hypersubstitution which maps F to the word x₁x₂x₁ or to the word x₂x₁x₂ belongs to M and that V is finitely based if it is locally finite.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 139-148
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On sets related to maximal clones
    Autorzy:
    Susanti, Yeni
    Denecke, Klaus
    Powiązania:
    https://bibliotekanauki.pl/articles/728974.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    operations preserving relations
    clones
    semigroups
    Opis:
    For an arbitrary h-ary relation ρ we are interested to express n-clone Polⁿρ in terms of some subsets of the set of all n-ary operations Oⁿ(A) on a finite set A, which are in general not clones but we can obtain Polⁿρ from these sets by using intersection and union. Therefore we specify the concept a function preserves a relation and moreover, we study the properties of this new concept and the connection between these sets and Polⁿρ. Particularly we study $R_{a̲,b}^{n,k}$ for arbitrary partial order relations, equivalence relations and central relations.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2012, 32, 1; 101-114
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    T-Varieties and Clones of T-terms
    Autorzy:
    Denecke, Klaus
    Jampachon, Prakit
    Powiązania:
    https://bibliotekanauki.pl/articles/729099.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    T-quasi constant algebra
    T-identity
    j-ideal
    T-hyperidentity
    clone of T-terms
    Opis:
    The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset T of $W_{τ}(X)$, the set of all terms of type τ, and consider identities from T×T. Since any variety can be described by one heterogenous algebra, its clone, we are also interested in the corresponding clone-like structure. Identities of the clone of a variety V correspond to M-hyperidentities for certain monoids M of hypersubstitutions. Therefore we will also investigate these monoids and the corresponding M-hyperidentities.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 1; 89-101
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Binary relations on the monoid of V-proper hypersubstitutions
    Autorzy:
    Denecke, Klaus
    Srithus, Rattana
    Powiązania:
    https://bibliotekanauki.pl/articles/729137.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    solid variety
    degree of proper hypersubstitutions
    isomorphism degree of proper hypersubstitutions
    Opis:
    In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2006, 26, 2; 233-251
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hypersatisfaction of formulas in agebraic systems
    Autorzy:
    Denecke, Klaus
    Phusanga, Dara
    Powiązania:
    https://bibliotekanauki.pl/articles/728760.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    algebraic system
    formula
    relational clone
    hyperformula
    Opis:
    In [2] the theory of hyperidentities and solid varieties was extended to algebraic systems and solid model classes of algebraic systems. The disadvantage of this approach is that it needs the concept of a formula system. In this paper we present a different approach which is based on the concept of a relational clone. The main result is a characterization of solid model classes of algebraic systems. The results will be applied to study the properties of the monoid of all hypersubstitutions of an ordered algebra.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2009, 29, 2; 123-151
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Complexity of hypersubstitutions and lattices of varieties
    Autorzy:
    Changphas, Thawhat
    Denecke, Klaus
    Powiązania:
    https://bibliotekanauki.pl/articles/728956.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitution
    left-seminearring
    complexity ofa hypersubstitution
    M-solid variety
    Opis:
    Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The complexity of a hypersubstitution can be measured by the complexity of the resulting terms. We prove that the set of all hypersubstitutions with a complexity greater than a given natural number forms a sub-left-seminearring of the left-seminearring of all hypersubstitutions of the considered type. Next we look to a special complexity measure, the operation symbol count op(t) of a term t and determine the greatest M-solid variety of semigroups where $M = H₂^{op}$ is the left-seminearring of all hypersubstitutions for which the number of operation symbols occurring in the resulting term is greater than or equal to 2. For every n ≥ 1 and for $M = Hₙ^{op}$ we determine the complete lattices of all M-solid varieties of semigroups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 1; 31-43
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regular elements and Greens relations in Menger algebras of terms
    Autorzy:
    Denecke, Klaus
    Jampachon, Prakit
    Powiązania:
    https://bibliotekanauki.pl/articles/729175.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    term
    superposition of terms
    Menger algebra
    regular element
    Green's relations
    Opis:
    Defining an (n+1)-ary superposition operation $S^n$ on the set $W_{τ}(X_n)$ of all n-ary terms of type τ, one obtains an algebra $n-clone τ := (W_{τ}(X_n); S^n, x_1, ..., x_n)$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^n$ there are different possibilities to define binary associative operations on the set $W_{τ}(X_n)$ and on the cartesian power $W_{τ}(X_n)^n$. In this paper we study idempotent and regular elements as well as Green's relations in semigroups of terms with these binary associative operations as fundamental operations.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2006, 26, 1; 85-109
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The semantical hyperunification problem
    Autorzy:
    Denecke, Klaus
    Koppitz, Jörg
    Wismath, Shelly
    Powiązania:
    https://bibliotekanauki.pl/articles/728730.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitution
    fully invariant congruence relation
    hyperunification problem
    Opis:
    A hypersubstitution of a fixed type τ maps n-ary operation symbols of the type to n-ary terms of the type. Such a mapping induces a unique mapping defined on the set of all terms of type t. The kernel of this induced mapping is called the kernel of the hypersubstitution, and it is a fully invariant congruence relation on the (absolutely free) term algebra $F_{τ}(X)$ of the considered type ([2]). If V is a variety of type τ, we consider the composition of the natural homomorphism with the mapping induced by a hypersubstitution. The kernel of this mapping is called the semantical kernel of the hypersubstitution with respect to the given variety. If the pair (s,t) of terms belongs to the semantical kernel of a hypersubstitution, then this hypersubstitution equalizes s and t with respect to the variety. Generalizing the concept of a unifier, we define a semantical hyperunifier for a pair of terms with respect to a variety. The problem of finding a semantical hyperunifier with respect to a given variety for any two terms is then called the semantical hyperunification problem.
    We prove that the semantical kernel of a hypersubstitution is a fully invariant congruence relation on the absolutely free algebra of the given type. Using this kernel, we define three relations between sets of hypersubstitutions and sets of varieties and introduce the Galois correspondences induced by these relations. Then we apply these general concepts to varieties of semigroups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 175-200
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
    Autorzy:
    Denecke, Klaus
    Hyndman, Jennifer
    Wismath, Shelly
    Powiązania:
    https://bibliotekanauki.pl/articles/728896.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitutions
    hyperidentities
    M-hyperidentities
    monoids of hypersubstitutions
    varieties
    solid varieties
    M-solid varieties of bands
    Galois correspondence
    Opis:
    Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 21-36
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Four-part semigroups - semigroups of Boolean operations
    Autorzy:
    Jampachon, Prakit
    Susanti, Yeni
    Denecke, Klaus
    Powiązania:
    https://bibliotekanauki.pl/articles/728987.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    four-part semigroup
    Boolean operation
    Opis:
    Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2012, 32, 1; 115-136
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The greatest regular-solid variety of semigroups % Dedicated to R. McKenzies 60$^th$ birthday %
    Autorzy:
    Denecke, Klaus
    Koppitz, Jörg
    Pabhapote, Nittiya
    Powiązania:
    https://bibliotekanauki.pl/articles/728806.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypersubstitutions
    terms
    regular-solid variety
    solid variety
    finite axiomatizability
    Opis:
    A regular hypersubstitution is a mapping which takes every $n_i$-ary operation symbol to an $n_i$-ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show that every variety of semigroups which is finitely based by hyperidentities is also finitely based by identities.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2008, 28, 1; 91-119
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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